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Table 2 Parameters

From: Evolution of selfish multicellularity: collective organisation of individual spatio-temporal regulatory strategies

Parameter

explanation

Values

\(L^2\)

lattice size

\(500 \times 500\) lattice sites

T

Boltzmann temperature

16 AUE

\(\lambda\)

cell stiffness

4.0 AUE/[lattice site]\(^2\)

\(A_T\)

cell target area

50 lattice sites

Cell adhesion

    \(J_\alpha\)

minimum J value between cells

4 AUE/[lattice site length]

    \(J_\alpha '\)

minimum J value between cell and medium

8 AUE/[lattice site length]

    \(\nu\)

length of receptor and ligand bitstring

24 bits

    \(\nu '\)

length ligand bitstring for medium adhesion

6 bits

Cell migration and chemotaxis

    \(\mu _p\)

strength of persistent migration

3.0 AUE

    \(\tau _p\)

duration of persistence vector

50 MCS

    \(\mu _{\chi }\)

strength of chemotaxis

1.0 AUE

    \(k_{\chi }\)

scaling factor chemoattractant gradient

5.0 molecules/[lattice site length]

Cell division

    \(\eta _{\text {init}}\)

time before cell in GRN state 1 can start growing

10000 MCS

    \(\eta _{\text {grow}}\)

time for cell in state 1 to grow to 2x \(A_T\) and divide

20000 MCS

Evolution

    \(\tau _s\)

duration of season

\(18 \times 10^4\) - \(50 \times 10^4\) MCS

    \(p_{\text {min}}\)

minimum probability of dying

0.05

    \(p_{\text {max}}\)

maximum probability of dying

1.0

    \(d_{\text {scale}}\)

distance from gradient peak where death probability is \(\frac{1}{2}\) maximum

40 or 80 [lattice site length]

    \(\mu _{R,I}\)

receptor and ligand mutation probability

0.01 per bit, per replication

    \(\mu _{\omega }\)

mutation probability of network parameters (w, f, \(r_a\))

0.02 per parameter, per replication

    \(\sigma\)

standard deviation of mutation size

0.05

  1. AUE Arbitrary Units of Energy (see the formulation of the Hamiltonian in the Cellular Potts Model section), lattice site unit of area, lattice site length unit of distance, MCS Monte Carlo Step (unit of time)